We study the Ricci flow in the setting of cohomogeneity one manifolds, i.e. a Riemannian manifold M with a group G acting isometrically such that the orbit space M/G is one-dimensional. Since isometries are preserved under the flow, the evolving metrics continue to be invariant. In several past works, this structure has been utilized to gain new information about the Ricci flow. In particular, we showed that in dimension 4 nonnegative sectional curvature is not preserved under the flow. We will describe the challenges in systematically studying Ricci flow on cohomogeneity one manifolds arising from both the degenerate parabolic nature of the Ricci flow PDE and the structure of invariant metrics on a cohomogeneity one manifold. We will also present a strategy to overcome these.